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Selected values of a continuous even function are shown below. ).

  1. Find , and .

    Definition of an even function: .

    Since then, by definition, as well.

  2. Sketch a possible graph of on the domain .

  3. Sketch another possible graph of on the domain .

    There are many ways to connect the points, just make sure you maintain symmetry over the -axis.

  4. Could the graph of be a parabolic function? If so, find a possible equation of . If not, explain.

    Can you draw a parabola through all of these points? Give it a try.

Use the eTool below to view the graphs of some possible functions.
Click the link at right for the full version of the eTool: Calc 1-70 HW eTool